Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into Euclidean space
Connections Workshop: New Frontiers in Curvature & Special Geometric Structures and Analysis August 21, 2024 - August 23, 2024
Location: SLMath: Eisenbud Auditorium, Online/Virtual
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Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into Euclidean space
We will prove that given an n-dimensional integral current space and a 1-Lipschitz map, from this space onto the n-dimensional Euclidean ball, that preserves the mass of the current and is injective on the boundary, then the map has to be an isometry. We deduce as a consequence the stability of the positive mass theorem for graphical manifolds as originally formulated by Huang--Lee--Sormani. (Joint work with G. Del Nin).
Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into Euclidean space
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